Derived algebraic geometry over En̳-rings
Author(s)Francis, John (John Nathan Kirkpatrick)
Massachusetts Institute of Technology. Dept. of Mathematics.
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We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, these theories converge to the derived algebraic geometry of Tobn-Vezzosi and Lurie. The class of spaces obtained by gluing En-rings form a geometric counterpart to En-categories, which are higher topological variants of braided monoidal categories. These spaces further provide a geometric language for the deformation theory of general E, structures. A version of the cotangent complex governs such deformation theories, and we relate its values to E&-Hochschild cohomology. In the affine case, this establishes a claim made by Kontsevich. Other applications include a geometric description of higher Drinfeld centers of SE-categories, explored in work with Ben-Zvi and Nadler.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.In title on t.p., double underscored "n" appears as subscript.Includes bibliographical references (p. 55-56).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology